- Email: [email protected]
Response to the Discussion on “The annual rate of independent events for the analysis of extreme wind speed, by R. Ian Harris”
Journal of Wind Engineering & Industrial Aerodynamics 164 (2017) 179–181
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Discussion
Response to the Discussion on “The annual rate of independent events for the analysis of extreme wind speed, by R. Ian Harris”
MARK
⁎
Alessio Torriellia, Maria Pia Repettob, , Giovanni Solarib a b
Siemens Wind Power A/S, WP OF EN ES TWS MMI, Fiskergade 1-9, 7100 Vejle, Denmark Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro, 1, 16145 Genoa, Italy
We greatly appreciate the contribution of this discusser. All the developments of our research on extreme wind speed have been inspired by the longstanding pioneering studies carried out by Harris and Cook. We are delighted that the discusser has taken up our idea of simulating long-term synthetic wind records (Torrielli et al., 2011, 2013) in his recent research (Harris, 2014) and this mutual interaction is still giving rise to evolutions and stimulating discussions. Firstly, we thank him to clarify his intention not to simulate the wind regime at Boscombe Down. On our side we wish to point out that the simulation algorithm used by Torrielli et al., (2011, 2013) provided a perfect matching of the spectrum of the wind speed and a good approximation of its parent distribution. The new simulation algorithm used by Torrielli et al. (2014) provided a perfect matching of the parent distribution and an almost perfect matching of the spectrum. Thus, also our method involves an excellent matching of these two key quantities. Secondly, the idea to simulate shorter length individual synthetic records and then to compute larger numbers of them to form an ensemble is very promising. Regarding the form of the standard reduced variate “y=h(v)-ln(r(V))” separating the curvature arising from the lack of convergence and that due to the correlation, is an idea that only the discusser with such an extensive experience could propose. We support this suggestion. In more general terms, however, we would like to comment on the discusser's remarks with regard to three points: 1) the relationship between the periodic variations of the mean wind speed and the parent distribution; 2) the relationship between the periodic variations of the mean wind speed and the extreme value distribution; and 3) the study of mixed populations. 1. Periodic variations of the mean wind speed versus parent distribution Torrielli et al. (2014) showed that the phase angles of the periodic components within a wind record are almost constant over different blocks of data, while their amplitudes show a non-negligible variation, which makes their ‘deterministic’ nature doubtful. In any case the authors believe that different parent distributions have to be used to
⁎
represent the sample collecting the measurable mean wind speed and the sample without the periodic components. To support this opinion an example based on real wind observations is proposed here. A wind speed record consisting of 406 days of continuous registration at the airport of Rome Ciampino (Italy) is analysed (10-min average speeds collected every 3 h. From the original signal (sample A) the harmonics having period of 1 yr, 24 h, 12 h and 8 h are removed, thus obtaining a second signal (sample B). Fig. 1 plots the empirical distributions relative to the two velocity samples on a Hybrid Weibull probability paper. The two samples have different distributions: sample A shows a linear trend, especially in the tail, whereas sample B shows a downward curvature. Thus, the parent distribution depends on the periodic components of the wind speed. If the periodic components are excluded by the analysis in terms of the auto-correlation function, a suitable parent distribution should be selected. In the light of these remarks authors cannot share the discusser's opinion on the lack of a link between the diurnal and annual variations of the wind speed and its parent distribution. 2. Periodic variations of the mean wind speed and the EV distribution To develop further this point authors refer to the study carried out by Torrielli et al. (2014). Almost 13,000 years of mean wind speeds were generated through an algorithm capable of superimposing a random part to the periodic variations of the velocity time series. Two datasets of annual maxima were selected: the first set collects the maxima extracted from the complete velocity time series (set A), while the second set collects the maxima extracted by eliminating the periodic components (set B). The empirical distributions related to the two datasets are plotted in Fig. 2. The two straight lines have a similar slope. This suggests that the absence of the periodic components does not alter significantly the shape of the upper tail of the EV distribution, but it does change the position of the curve with respect to the velocity axis. It is worth noting the similarity between Fig. 2 and Figures 3–7 presented by the discusser. The authors fear that the shift of the
Corresponding author. E-mail addresses: [email protected] (A. Torrielli), [email protected] (M.P. Repetto), [email protected] (G. Solari).
http://dx.doi.org/10.1016/j.jweia.2017.01.016
0167-6105/ © 2017 Elsevier Ltd. All rights reserved.
Journal of Wind Engineering & Industrial Aerodynamics 164 (2017) 179–181
A. Torrielli et al.
Fig. 1. Hibrid Weibull (HW) distribution – Ciampino airport wind record.
such as thunderstorms. For instance, De Gaetano et al. (2014) showed that in correspondence of thunderstorm gust fronts, which last for a few minutes, the mean wind velocity may be in the order of 5–10 m/s, whereas the peak wind velocity may reach 35–40 m/s. Thus, any analysis carried out in terms of mean wind speeds cannot be representative of such short transient events. In this sense an evolution from the examples developed by Harris and Cook (2014), where the OEN method was formulated, and the Adelaide study carried out by Cook (2015) was noted. In the first paper the analysis of the Roma Ciampino dataset led to 3 OENs, one of which is related to thunderstorms It is not clear, however, in what way a method that inspects mean wind speeds may extract such an information. In the second paper, instead, the analysis of the Adelaide dataset led to identify a set of 4 or 5 climatic conditions whose time variation is slow enough to be properly identified based on mean wind speeds. This analysis is amazing. 4. Conclusions The authors admire the quality and elegance of the theoretical remarks of the discusser, probably the only one able to perform such evaluations with this level of skill. On the other hand they point out that the discusser's wind simulation is based on theoretical and a-priori defined parent distributions and auto-correlation functions, which neglect dominant features as the periodic variations of the wind speed. In this closure and in a previous paper (Torrielli et al., 2014) authors stressed and tried to demonstrate that the presence of these components cannot be ignored because, in this case, the simulations and their analysis do not concern the physical wind phenomenon. Indeed, all the research carried out by the authors has been inspired to focus on physical reality. In this regard, the final results provided by Figure 4 of the paper under discussion show that the ARIE (Annual Rate of Independent Events) EV distribution offers a perfect matching with the simulated data and this precision is definitely greater that exhibited by any other previous EV model. The paper recognizes however, that this model suffers a high sensitivity to the propagation of the uncertainties. Perhaps the time may be ripe to develop new evaluations aiming to move these two different viewpoints towards convergence. Just to carry out a more consistent theoretical analysis and a better comparison with the results provided by the discusser, the effect of removing the periodic components should be studied. On the other hand, it should be great if, retaining the robust theoretical bases, the discusser could implement a complete simulation of the wind speed that includes the periodic components, just to show how much representative the
Fig. 2. Gumbel plot of EV distributions.
discusser's distributions may be due to the lack of the periodic components. Of course, a better evaluation needs more time for detailed analyses. In view of these remarks and confirming what they previously wrote (Torrielli et al., 2014) the authors do not share the discusser's opinion about the lack of a link between the diurnal and annual variations of the wind speed and the EV distribution. They also note that the limiting value of the annual rate of the independent events cannot be seen in Figures 3–7 of the discusser, because these do not plot real wind speeds. 3. Mixed populations The authors appreciate the innovation and fascination of the OEN method (Harris and Cook, 2014) and its potential to identify and separate the parent distributions of the components (not the data) of a mixed population. As the discusser claims, this method is very attractive to identify and separate the synoptic phenomena that characterize a mixed climate, including those related to the daily and seasonal solar cycles. Instead, the authors maintain that this method cannot identify and separate synoptic from non-synoptic phenomena 180
Journal of Wind Engineering & Industrial Aerodynamics 164 (2017) 179–181
A. Torrielli et al.
Harris, R.I., 2014. A simulation method for the macro-meteorological wind speed and the implications for extreme value analysis. J. Wind Eng. Ind. Aerod. 125, 145–155. Harris, R.I., Cook, N.J., 2014. The parent wind speed distribution: why Weibull? J. Wind Eng. Ind. Aerod. 131, 72–87. Torrielli, A., Repetto, M.P., Solari, G., 2011. Long-term simulations of the mean wind velocity. J. Wind Eng. Ind. Aerod. 99, 1139–1150. Torrielli, A., Repetto, M.P., Solari, G., 2013. Extreme wind speeds from long-term synthetic records. J. Wind Eng. Ind. Aerod. 115, 22–38. Torrielli, A., Repetto, M.P., Solari, G., 2014. A refined analysis and simulation of the wind speed macro-meteorological components. J. Wind Eng. Ind. Aerod. 132, 54–65.
evaluations may be without them. This could be a milestone towards a correct understanding and modelling of the extreme wind speed. References Cook, N.J., 2015. A statistical model of the seasonal-diurnal wind climate at Adelaide. Austral. Meteor. Ocean. J. 65, 206–232. De Gaetano, P., Repetto, M.P., Repetto, T., Solari, G., 2014. Separation and classification of extreme wind events from anemometric records. J. Wind Eng. Ind. Aerod. 126, 132–143.
181
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Discussion
Response to the Discussion on “The annual rate of independent events for the analysis of extreme wind speed, by R. Ian Harris”
MARK
⁎
Alessio Torriellia, Maria Pia Repettob, , Giovanni Solarib a b
Siemens Wind Power A/S, WP OF EN ES TWS MMI, Fiskergade 1-9, 7100 Vejle, Denmark Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro, 1, 16145 Genoa, Italy
We greatly appreciate the contribution of this discusser. All the developments of our research on extreme wind speed have been inspired by the longstanding pioneering studies carried out by Harris and Cook. We are delighted that the discusser has taken up our idea of simulating long-term synthetic wind records (Torrielli et al., 2011, 2013) in his recent research (Harris, 2014) and this mutual interaction is still giving rise to evolutions and stimulating discussions. Firstly, we thank him to clarify his intention not to simulate the wind regime at Boscombe Down. On our side we wish to point out that the simulation algorithm used by Torrielli et al., (2011, 2013) provided a perfect matching of the spectrum of the wind speed and a good approximation of its parent distribution. The new simulation algorithm used by Torrielli et al. (2014) provided a perfect matching of the parent distribution and an almost perfect matching of the spectrum. Thus, also our method involves an excellent matching of these two key quantities. Secondly, the idea to simulate shorter length individual synthetic records and then to compute larger numbers of them to form an ensemble is very promising. Regarding the form of the standard reduced variate “y=h(v)-ln(r(V))” separating the curvature arising from the lack of convergence and that due to the correlation, is an idea that only the discusser with such an extensive experience could propose. We support this suggestion. In more general terms, however, we would like to comment on the discusser's remarks with regard to three points: 1) the relationship between the periodic variations of the mean wind speed and the parent distribution; 2) the relationship between the periodic variations of the mean wind speed and the extreme value distribution; and 3) the study of mixed populations. 1. Periodic variations of the mean wind speed versus parent distribution Torrielli et al. (2014) showed that the phase angles of the periodic components within a wind record are almost constant over different blocks of data, while their amplitudes show a non-negligible variation, which makes their ‘deterministic’ nature doubtful. In any case the authors believe that different parent distributions have to be used to
⁎
represent the sample collecting the measurable mean wind speed and the sample without the periodic components. To support this opinion an example based on real wind observations is proposed here. A wind speed record consisting of 406 days of continuous registration at the airport of Rome Ciampino (Italy) is analysed (10-min average speeds collected every 3 h. From the original signal (sample A) the harmonics having period of 1 yr, 24 h, 12 h and 8 h are removed, thus obtaining a second signal (sample B). Fig. 1 plots the empirical distributions relative to the two velocity samples on a Hybrid Weibull probability paper. The two samples have different distributions: sample A shows a linear trend, especially in the tail, whereas sample B shows a downward curvature. Thus, the parent distribution depends on the periodic components of the wind speed. If the periodic components are excluded by the analysis in terms of the auto-correlation function, a suitable parent distribution should be selected. In the light of these remarks authors cannot share the discusser's opinion on the lack of a link between the diurnal and annual variations of the wind speed and its parent distribution. 2. Periodic variations of the mean wind speed and the EV distribution To develop further this point authors refer to the study carried out by Torrielli et al. (2014). Almost 13,000 years of mean wind speeds were generated through an algorithm capable of superimposing a random part to the periodic variations of the velocity time series. Two datasets of annual maxima were selected: the first set collects the maxima extracted from the complete velocity time series (set A), while the second set collects the maxima extracted by eliminating the periodic components (set B). The empirical distributions related to the two datasets are plotted in Fig. 2. The two straight lines have a similar slope. This suggests that the absence of the periodic components does not alter significantly the shape of the upper tail of the EV distribution, but it does change the position of the curve with respect to the velocity axis. It is worth noting the similarity between Fig. 2 and Figures 3–7 presented by the discusser. The authors fear that the shift of the
Corresponding author. E-mail addresses: [email protected] (A. Torrielli), [email protected] (M.P. Repetto), [email protected] (G. Solari).
http://dx.doi.org/10.1016/j.jweia.2017.01.016
0167-6105/ © 2017 Elsevier Ltd. All rights reserved.
Journal of Wind Engineering & Industrial Aerodynamics 164 (2017) 179–181
A. Torrielli et al.
Fig. 1. Hibrid Weibull (HW) distribution – Ciampino airport wind record.
such as thunderstorms. For instance, De Gaetano et al. (2014) showed that in correspondence of thunderstorm gust fronts, which last for a few minutes, the mean wind velocity may be in the order of 5–10 m/s, whereas the peak wind velocity may reach 35–40 m/s. Thus, any analysis carried out in terms of mean wind speeds cannot be representative of such short transient events. In this sense an evolution from the examples developed by Harris and Cook (2014), where the OEN method was formulated, and the Adelaide study carried out by Cook (2015) was noted. In the first paper the analysis of the Roma Ciampino dataset led to 3 OENs, one of which is related to thunderstorms It is not clear, however, in what way a method that inspects mean wind speeds may extract such an information. In the second paper, instead, the analysis of the Adelaide dataset led to identify a set of 4 or 5 climatic conditions whose time variation is slow enough to be properly identified based on mean wind speeds. This analysis is amazing. 4. Conclusions The authors admire the quality and elegance of the theoretical remarks of the discusser, probably the only one able to perform such evaluations with this level of skill. On the other hand they point out that the discusser's wind simulation is based on theoretical and a-priori defined parent distributions and auto-correlation functions, which neglect dominant features as the periodic variations of the wind speed. In this closure and in a previous paper (Torrielli et al., 2014) authors stressed and tried to demonstrate that the presence of these components cannot be ignored because, in this case, the simulations and their analysis do not concern the physical wind phenomenon. Indeed, all the research carried out by the authors has been inspired to focus on physical reality. In this regard, the final results provided by Figure 4 of the paper under discussion show that the ARIE (Annual Rate of Independent Events) EV distribution offers a perfect matching with the simulated data and this precision is definitely greater that exhibited by any other previous EV model. The paper recognizes however, that this model suffers a high sensitivity to the propagation of the uncertainties. Perhaps the time may be ripe to develop new evaluations aiming to move these two different viewpoints towards convergence. Just to carry out a more consistent theoretical analysis and a better comparison with the results provided by the discusser, the effect of removing the periodic components should be studied. On the other hand, it should be great if, retaining the robust theoretical bases, the discusser could implement a complete simulation of the wind speed that includes the periodic components, just to show how much representative the
Fig. 2. Gumbel plot of EV distributions.
discusser's distributions may be due to the lack of the periodic components. Of course, a better evaluation needs more time for detailed analyses. In view of these remarks and confirming what they previously wrote (Torrielli et al., 2014) the authors do not share the discusser's opinion about the lack of a link between the diurnal and annual variations of the wind speed and the EV distribution. They also note that the limiting value of the annual rate of the independent events cannot be seen in Figures 3–7 of the discusser, because these do not plot real wind speeds. 3. Mixed populations The authors appreciate the innovation and fascination of the OEN method (Harris and Cook, 2014) and its potential to identify and separate the parent distributions of the components (not the data) of a mixed population. As the discusser claims, this method is very attractive to identify and separate the synoptic phenomena that characterize a mixed climate, including those related to the daily and seasonal solar cycles. Instead, the authors maintain that this method cannot identify and separate synoptic from non-synoptic phenomena 180
Journal of Wind Engineering & Industrial Aerodynamics 164 (2017) 179–181
A. Torrielli et al.
Harris, R.I., 2014. A simulation method for the macro-meteorological wind speed and the implications for extreme value analysis. J. Wind Eng. Ind. Aerod. 125, 145–155. Harris, R.I., Cook, N.J., 2014. The parent wind speed distribution: why Weibull? J. Wind Eng. Ind. Aerod. 131, 72–87. Torrielli, A., Repetto, M.P., Solari, G., 2011. Long-term simulations of the mean wind velocity. J. Wind Eng. Ind. Aerod. 99, 1139–1150. Torrielli, A., Repetto, M.P., Solari, G., 2013. Extreme wind speeds from long-term synthetic records. J. Wind Eng. Ind. Aerod. 115, 22–38. Torrielli, A., Repetto, M.P., Solari, G., 2014. A refined analysis and simulation of the wind speed macro-meteorological components. J. Wind Eng. Ind. Aerod. 132, 54–65.
evaluations may be without them. This could be a milestone towards a correct understanding and modelling of the extreme wind speed. References Cook, N.J., 2015. A statistical model of the seasonal-diurnal wind climate at Adelaide. Austral. Meteor. Ocean. J. 65, 206–232. De Gaetano, P., Repetto, M.P., Repetto, T., Solari, G., 2014. Separation and classification of extreme wind events from anemometric records. J. Wind Eng. Ind. Aerod. 126, 132–143.
181